Pass out the handout Exploring Rotations in the Plane. Click below to watch a short tutorial video on how to rotate the triangle in question one using tracing paper.
As a class, walk through the rotation in question one using the document camera and moving about the room between steps to ensure all students are following along with making mistakes. After completing the first rotation completely and correctly hold a whole class discussion to begin consolidating student learning: Discuss the following questions: “Look at your pre-image TOP and image T’O’P’, are the two triangles congruent? How can you prove your answer?” Allow one minute of think and talk time between partners in groups. Then, go to each student group individually and allow them to answer these two questions directly to you. Next, address the entire class again and ask, “Are rotations an example of rigid motion? What does it mean to be a rigid motion?”
After concluding the group discussion, allow students to work on the next two rotations within their group. I usually allow about ten minutes to work as I move about the room assessing progress, helping students who typically need additional assistance to be successful, and creating my experts who will present during the mini wrap up session at the end of the given time.
After about 10 minutes of time to work students should be ready to discuss their answers to the last two rotations. Again, work with student groups as they complete these questions and pick or create your experts who will present during whole group discussion. If you do not find enough student experts to share answers then create some by questioning and helping student groups - helping struggling students to become experts, then asking them share out during group discussion is a great way to build confidence and enthusiasm for math.
Ask two different student groups to come to the document camera and present their rotations of the trapezoid and pentagon. Ask the following questions about the pentagon in rotation number three: “Look at the two pentagons LEARN and L’E’A’R’N’, what transformation other than a rotation does this resemble? (Answer: a reflection). “Is there a reflection that would map pentagon LEARN directly on top of pentagon L’E’A’R’N’ – prove it by finding the line of reflection or by explaining why you couldn’t map with a reflection.
Homework: If there is not enough time to complete and discuss the final questions: “Is there a reflection that would map pentagon LEARN directly on top of pentagon L’E’A’R’N’ – prove it by finding the line of reflection or by explaining why you couldn’t map with a reflection. “ Then this is homework for the class. My students all have Edmodo.com accounts and I often like to pose discussion questions to the class and have them discuss online through Edmodo that night. This would be a good Edmodo discussion question. Students could even show an example of the reflection by taking a picture of their work using a phone or ipad and then upload to Edmodo as part of their discussion. Sometimes, I encourage participation by offering a soda to the first person with a correct and very complete answer.